The present paper is intended to be the first of a series on the species of Pachylomidium from all over the world. It has been prepared under supervision of Dr. P. A. Florschütz (Instituut voor Systematische Plantkunde, Heidelberglaan 2, Utrecht). The species of Pachylomidium are characterised by leaves which are completely or nearly completely bordered, with a nerve which nearly or completely reaches the apex, smooth cells and a pluristratose border. The species of this section grow exclusively near running water and are inundated during part of the year. Unfortunately there are some species which are more or less transitional between this section and other ones. I will deal with these problems more extensively in a following paper.